JEE Main & Advanced Physics Vectors Question Bank Fundamentals of Vectors

  • question_answer If \[A=3\hat{i}+4\hat{j}\] and \[B=7\hat{i}+24\hat{j},\]the vector having the same magnitude as B and parallel to A is

    A)            \[5\hat{i}+20\hat{j}\]

    B)                                      \[15\hat{i}+10\hat{j}\]

    C)            \[20\hat{i}+15\hat{j}\]    

    D)            \[15\hat{i}+20\hat{j}\]

    Correct Answer: D

    Solution :

                 \[|B|\,=\sqrt{{{7}^{2}}+{{(24)}^{2}}}\] \[=\sqrt{625}\] \[=25\]                    Unit vector in the direction of A will be \[\hat{A}=\frac{3\hat{i}+4\hat{j}}{5}\]                    So required vector =\[25\left( \frac{3\hat{i}+4\hat{j}}{5} \right)\,\] \[=15\hat{i}+20\hat{j}\]

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